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A lift of the Chern-Simons functional and its application to equivariant Floer homology Anderson, Vaughn
Abstract
We investigate the gauge theory of 3- and 4- manifolds. A lift of the Chern-Simons
functional for fiat connections on a principal SU(2)-bundle over a homology 3-sphere
Y is constructed,
putting
strong restrictions on the existence of low-dimensional
instan
ton moduli spaces over the cylinder R x Y. The value of this lift is computed for the
Brieskorn spheres Σ(p, q, pqk — 1), and there is found to be one and only one flat
con
nection of Floer index 1 with positive Chern-Simons functional. This fact is applied to
the computation of the equivariant Floer homology
HFG,*(Σ(2,
3, 6k — 1)) showing
that
there are connections of index 1 and 5 with non-trivial boundary in the equivariant Floer
homology. Specializing to the case k
=
2, we obtain vanishing of
HFG,₄*₊₁(Σ(2,
3, 11)).
Item Metadata
| Title |
A lift of the Chern-Simons functional and its application to equivariant Floer homology
|
| Creator | |
| Publisher |
University of British Columbia
|
| Date Issued |
1995
|
| Description |
We investigate the gauge theory of 3- and 4- manifolds. A lift of the Chern-Simons
functional for fiat connections on a principal SU(2)-bundle over a homology 3-sphere
Y is constructed,
putting
strong restrictions on the existence of low-dimensional
instan
ton moduli spaces over the cylinder R x Y. The value of this lift is computed for the
Brieskorn spheres Σ(p, q, pqk — 1), and there is found to be one and only one flat
con
nection of Floer index 1 with positive Chern-Simons functional. This fact is applied to
the computation of the equivariant Floer homology
HFG,*(Σ(2,
3, 6k — 1)) showing
that
there are connections of index 1 and 5 with non-trivial boundary in the equivariant Floer
homology. Specializing to the case k
=
2, we obtain vanishing of
HFG,₄*₊₁(Σ(2,
3, 11)).
|
| Extent |
1564684 bytes
|
| Genre | |
| Type | |
| File Format |
application/pdf
|
| Language |
eng
|
| Date Available |
2009-06-03
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
| DOI |
10.14288/1.0080023
|
| URI | |
| Degree (Theses) | |
| Program (Theses) | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
|
| Graduation Date |
1995-11
|
| Campus | |
| Scholarly Level |
Graduate
|
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.